Multiples
What is a multiple?
A number you get when you multiply a number by a whole number.
What is a factor?
A number that divides evenly into another number.
In the number 4,562, what does the 5 represent?
500 (five hundreds).
What is the box method used for in multiplication?
It’s a way to break numbers into parts (place values) and multiply each part before adding the partial products.
What does the partial quotients method mean in division?
It’s when you break a division problem into easier parts by subtracting partial products of the divisor until there’s nothing left (or a small remainder).
Name the first five multiples of 4.
4, 8, 12, 16, 20.
How many tens are in one hundred?
10 tens.
Use the box method to solve:
23 × 4 = ?
(20 × 4) + (3 × 4) = 80 + 12 = 92.
Use partial quotients to solve: 84 ÷ 7.
7 × 10 = 70 → 84 - 70 = 14
7 × 2 = 14 → 14 - 14 = 0
Add partial quotients: 10 + 2 = 12.
True or False: 36 is a multiple of 9.
True! (9 × 4 = 36)
True or False: 7 is a factor of 28.
True! (7 × 4 = 28)
The 6 in 6,000 is how many times greater than the 6 in 600?
10 times greater.
When multiplying 36 × 7, what are the partial products?
(30 × 7) = 210 and (6 × 7) = 42.
In 96 ÷ 8, what are the partial products (or “chunks”) you could use to solve?
8 × 10 = 80 → remainder 16
8 × 2 = 16 → remainder 0
Quotient = 12.
What is the smallest common multiple of 3 and 5?
15.
Which number is prime — 9, 11, or 15?
11 (it only has factors 1 and 11).
Round 7,846 to the nearest hundred.
7,800.
Use the box method to solve 24 × 13.
(20 × 10) = 200
(20 × 3) = 60
(4 × 10) = 40
(4 × 3) = 12
Add them up: 200 + 60 + 40 + 12 = 312.
Solve 196 ÷ 4 using the partial quotients method.
4 × 40 = 160 → 196 - 160 = 36
4 × 9 = 36 → 36 - 36 = 0
Add partial quotients: 40 + 9 = 49.
A mystery number is a multiple of both 6 and 8. What’s the smallest it could be?
24
A number has the factors 1, 2, 3, and 6. What’s the number?
6
Write a number that has a 3 in the thousands place, a 5 in the hundreds place, and a 2 in the tens place.
3,520.
Explain how the partial product method helps you check your work when multiplying large numbers.
It shows each smaller multiplication step separately, making it easier to spot mistakes and understand how the digits combine to form the final product.
Explain how partial quotients and partial products are similar.
Both break numbers into smaller, easier chunks using place value — multiplication builds up with partial products, and division breaks down with partial quotients.